A design method for temperature gradient compensation electrode of CO2 laser amplifier

Abstract

The present application relates to the field of laser technology and provides a method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier. The laser amplifier is used for an extreme ultraviolet lithography light source, comprising: constructing an electrode width of the laser amplifier in the downstream direction of the axial direction from the starting position to the downstream position; x The arc function at the starting position is based on the electrode width. x The electrode structure is designed based on the radian function at the electrode, so that the electrode extends in a spiral along the axial direction, and the radian corresponding to the electrode width increases along the axial direction. By designing a spiral electrode structure with an increasing radian along the axial direction of gas flow, the electric field intensity E in the discharge area changes along the axial direction to compensate for the decrease in gas particle number density N caused by the axial thermal effect, maintain the discharge condition E / N at a certain level, and reduce the impact of the axial temperature gradient on the axial discharge uniformity of the gas.

Description

Technical Field

[0001] The present application relates to the field of laser technology, and in particular to a method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier. Background Art

[0002] During the operation of a high-power laser amplifier, in order to ensure that the laser obtains sufficiently high gain, it is necessary to compensate for the thermal expansion caused by the accumulation of gas discharge temperature to ensure the consistency of the gas discharge area. With the urgent need for industrial development to increase the power of CO2 lasers, the RF power deposition of CO2 laser amplifiers is required to increase. Under these conditions, the temperature at the downwind outlet of the CO2 laser amplifier discharge area gradually increases, and the particle number density gradually decreases along the axial direction, making it difficult to ensure the consistency of the gas discharge area. Currently, most of the methods use a combination of fans and heat exchangers to cool the CO2 laser amplifier through a large flow of gas circulating inside the CO2 laser amplifier to reduce the temperature gradient in the discharge area and alleviate the thermal expansion caused by the axial thermal gradient of the RF fast axial flow CO2 laser amplifier.

[0003] However, the gas mass flow rate that the current CO2 laser amplifier blower can provide is approaching its upper limit, and the thermal expansion of the plasma makes it difficult to meet the demand for further power increases. Further increasing the blower speed in high-power CO2 laser amplifiers is already very difficult in the current industry. Further increasing the RF discharge injection power will increase the temperature gradient between the upper and lower air outlets, resulting in an uneven distribution of RF glow discharge plasma particle density inside the glass tube during operation, affecting the laser gain. The flow field wind speed in high-power CO2 laser amplifiers is currently close to the speed of sound. If the wind speed reaches supersonic speed or above, shock waves and sonic barriers will occur, seriously affecting the discharge process. This makes it difficult to meet the demand for further power increases. Summary of the Invention

[0004] This application provides a design method for a temperature gradient effect compensation electrode for a CO2 laser amplifier to solve at least one of the above-mentioned technical problems. The details are as follows:

[0005] Some embodiments of the present application provide a method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier, wherein the laser amplifier is applied to an extreme ultraviolet lithography light source, including:

[0006] Construct the electrode width of the laser amplifier along the axial downstream direction from the starting position x The radian function at :

[0007]

[0008] in, k is the electrostatic force constant, Indicates the wall thickness of the glass discharge tube. is the electric power injection at the starting position of the discharge area, k B is the Boltzmann constant, L 0 is the total length of the electrode ω is the RF angular frequency, ε is the dielectric constant of quartz glass, L 0 is the total length of the electrode, a is the discharge threshold, P is the discharge gas pressure, d is the discharge distance, U 0 is the discharge electrode voltage, C 气体 is the specific heat capacity of the gas, v 气体 is the gas flow rate, S is the cross-sectional area of ​​the discharge glass tube, is the gas density, is the gas temperature at the starting position of the discharge region;

[0009] According to the electrode width distance from the starting position x The radian function at The electrode structure is designed so that the electrode extends in an axial spiral and the arc corresponding to the electrode width along the axial direction increases gradually.

[0010] In some embodiments, the electrodes include a positive electrode extending in a spiral along the axial direction and a negative electrode extending in a spiral along the axial direction, and a distance between the positive electrode and the negative electrode remains constant in the axial direction.

[0011] In some embodiments, the positive electrode and the negative electrode are symmetrically arranged outside the discharge tube.

[0012] In some embodiments, the electrode includes a starting end and an ending end extending in an axial spiral direction, and the spiral extension angle from the starting end to the ending end in the circumferential direction is less than 360 degrees.

[0013] In some embodiments, the spiral extension angle from the starting end to the ending end in the circumferential direction is less than 180 degrees.

[0014] In some embodiments, the curvature of the electrode from the starting end to the ending end is equal.

[0015] In some embodiments, the widths of the positive electrode and the negative electrode from the starting end to the ending end are symmetrically equal along the center of the discharge tube.

[0016] In some embodiments, the width of the positive electrode and the negative electrode at the starting end in the flattened state is smaller than the width of the ending end.

[0017] In some embodiments, the width of the positive electrode and the negative electrode at the starting end in the flattened state is smaller than the width of the ending end.

[0018] In some embodiments, under a power injection of 10 kW, the arc of the electrode at the starting end is 15 degrees, and the arc at a distance of 220 mm downstream is 20 degrees.

[0019] In some embodiments, the electrode width of the laser amplifier in the downstream direction is from the starting position to the x The radian function at ,include:

[0020] Constructing the laser amplifier along the axial distance x Temperature gradient function at :

[0021]

[0022] in, P x is the axial distance of the discharge area from the starting position x The electric power injection at T x The axial distance of the discharge area from the starting position x The gas temperature at is the gas temperature at the starting position of the discharge region;

[0023] Constructing spiral electrode along the axial distance x The radian function at Temperature gradient function Relationship:

[0024]

[0025] Ignore the temperature quartic term Then, the electrode width of the laser amplifier in the downstream direction is obtained from the starting position. x The radian function at :

[0026] 。

[0027] Compared with the related art, the above solution of the embodiment of the present application has at least the following beneficial effects:

[0028] This application proposes a method for designing electrodes to compensate for temperature gradient effects in CO2 laser amplifiers through theoretical derivation. This method results in an electrode structure in which the electrode extends in a spiral axial direction, with the arc increasing along the axial electrode width. By designing a spiral electrode structure with an increasing arc along the gas flow direction, this application achieves an axial change in the electric field strength E in the discharge region to compensate for the decrease in gas particle density N caused by axial thermal effects, maintain the discharge condition E / N at a certain level, and reduce the impact of axial temperature gradients on the uniformity of axial gas discharge. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings are incorporated into and constitute a part of the specification, illustrating embodiments consistent with the present application and, together with the specification, explaining the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and those skilled in the art can derive other drawings based on these drawings without inventive effort. In the drawings:

[0030] Figure 1 Flowchart of a method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier according to some embodiments of the present application.

[0031] Figure 2 Schematic diagram of the spiral electrode structure provided in some embodiments of the present application.

[0032] Figure 3 This is a schematic diagram of the structure of the spiral electrode in the flattened state provided in some embodiments of the present application.

[0033] Figure 4 Schematic diagram of the cross-sectional structure of the spiral electrode provided in some embodiments of the present application.

[0034] Description of reference numerals:

[0035] 1: Downwind port; 2: Upwind port; 3: Spiral gradient electrode; 4: Polytetrafluoroethylene electrode holder; 5: Discharge tube; 32: Ending end; 31: Starting end. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of this application more clear, this application will be further described in detail below with reference to the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0037] The terms used in the examples of this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms "a," "the," and "the" used in the examples of this application and the appended claims are also intended to include plural forms, and unless the context clearly indicates otherwise, "a plurality" generally includes at least two.

[0038] It should be understood that the term "and / or" as used herein is merely a description of the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the associated objects are in an "or" relationship.

[0039] It should be understood that although the terms first, second, third, etc. may be used to describe in the embodiments of the present application, these should not be limited to these terms. These terms are only used to distinguish. For example, without departing from the scope of the embodiments of the present application, the first may also be referred to as the second, and similarly, the second may also be referred to as the first.

[0040] It should also be noted that the terms "include," "comprises," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a product or device comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such product or device. In the absence of further limitations, an element defined by the phrase "comprising a" does not exclude the presence of other identical elements in the product or device comprising the element.

[0041] Extreme ultraviolet lithography (EUVL) is a key technology for high-end chip manufacturing. Laser Produced Plasma-Extreme Ultraviolet (LPP-EUV) sources are currently the only commercially available EUV lithography sources. LPP-EUV sources utilize a pre-main pulse laser to irradiate tin droplets, generating over 200W of EUV light. To improve EUV conversion efficiency, the main pulse laser typically utilizes a master oscillator power amplifier (MOPA)-based CO2 laser to generate 10.6μm pulses with an average power exceeding 20kW. In the MOPA system, the seed laser is amplified by an RF-excited fast axial flow CO2 laser amplifier. Gain is achieved through glow discharge within multiple gas discharge tubes, where a rapidly flowing CO2, N2, and He gas mixture flows along the optical axis under an RF electric field.

[0042] In an RF fast axial flow CO2 laser amplifier, the laser gains gain in a plasma generated by RF capacitively coupled dielectric barrier discharge at a gas pressure of the order of 10 kPa. The state of the dielectric barrier discharge plasma is related to the electric field intensity E and the ratio E / N of the gas particle number density N. During the operation of the laser amplifier, in order to ensure that the laser obtains sufficiently high gain, it is necessary to compensate for the thermal expansion caused by the accumulation of gas discharge temperature to ensure that the E / N ratio in the gas discharge region is consistent. With the urgent need for increased CO2 laser power due to industrial development, the RF electric power deposition of the CO2 laser amplifier is required to be increased. Under these conditions, the temperature of the downwind outlet of the CO2 laser amplifier discharge region gradually increases, and the particle number density N gradually decreases along the axial direction. However, the gas mass flow rate that can be provided by the current CO2 laser amplifier blower is close to the upper limit, and the thermal expansion of the plasma cannot meet the demand for further power increase.

[0043] In kilowatt-class low-power RF fast axial flow CO2 laser amplifiers, an axially tilted gas discharge electrode structure is used to compensate for the thermal expansion of the discharge plasma due to temperature accumulation in the axial direction. During the gas discharge process, the discharge plasma flowing axially generates heat due to the continuous injection of RF power, which in turn produces a temperature gradient in the axial region of the discharge electrode. The axially tilted discharge electrodes can reduce the electric field strength E in the discharge region by increasing the distance between the electrodes, compensating for the decrease in the particle number density N caused by thermal expansion of the discharge plasma, maintaining the E / N ratio in the laser amplifier discharge region at the same level, and improving the RF power deposition of the CO2 laser amplifier.

[0044] In high-power RF fast axial flow CO2 laser amplifiers above 10,000 watts, most of them currently use a combination of fans and heat exchangers. The large flow of gas inside the CO2 laser amplifier is circulated for cooling to reduce the temperature gradient in the discharge area and alleviate the thermal expansion caused by the axial thermal gradient of the RF fast axial flow CO2 laser amplifier.

[0045] Currently, the temperature of the internal discharge region of CO2 laser amplifiers exceeding 10,000 watts is maintained through gas circulation cooling. The temperature gradient in the discharge region is primarily regulated by adjusting the mass flow rate within the discharge tube. Specifically, under the condition of constant deposited electrical power in the discharge region, the greater the mass flow rate, the lower the temperature gradient in the discharge region. The downflow temperature is solely dependent on the RF discharge power injection and the temperature gradient. However, the gas mass flow rate that the current CO2 laser amplifier blower can provide is approaching its upper limit. Further increasing the blower speed in high-power CO2 laser amplifiers is already very difficult in the current industry. Further increasing the RF discharge injection power would increase the temperature gradient between the upflow and downflow ports, leading to uneven distribution of RF glow discharge plasma particle density within the glass tube during operation, thus affecting laser gain. Currently, the flow field wind speed in high-power CO2 laser amplifiers is already approaching the speed of sound. If the wind speed reaches supersonic speeds or above, shock waves and sonic barriers will occur, severely impacting the discharge process. This makes it difficult to meet the demand for further power increases.

[0046] Unlike kilowatt-class low-power RF fast axial flow CO2 laser amplifiers, in 10,000-watt-class high-power RF fast axial flow CO2 laser amplifiers, the discharge electrodes in a spiral structure surrounding the glass tube are required to maintain symmetry in the circumferential discharge uniformity of the gas discharge. Unlike kilowatt-class laser amplifiers, an axially tilted linear electrode structure cannot be used. Related gas discharge experiments have shown that under the high-power RF injection conditions of 10,000-watt laser amplifiers, the tilted electrode ensures the uniformity of the circumferential gain of the discharge tube. However, due to metal stress, the processing accuracy of the axially widened spiral electrode cannot be guaranteed. Therefore, the tilted electrode design used to compensate for the axial temperature gradient in kilowatt-class laser amplifiers cannot be simply applied to the spiral electrodes in 10,000-watt laser amplifiers. The local thermal expansion of the discharge plasma caused by the temperature gradient cannot be alleviated, and the discharge is more likely to occur at the downwind outlet, reducing the discharge uniformity.

[0047] Based on this, the present invention starts from the electrode structure and designs a spiral discharge electrode structure with an increased axial curvature. Within a certain RF electric power injection range, it can compensate for the thermal expansion of the discharge plasma caused by the axial temperature gradient, improve the E / N consistency of the upper and lower tuyere discharge areas, and is suitable for high-power RF fast axial flow CO2 laser amplifiers.

[0048] Based on the fact that the mass flow rate of the fan in the existing CO2 laser amplifier is close to the upper limit, the present invention reduces the influence of the thermal effect of the discharge module in the CO2 laser amplifier on the E / N ratio of the discharge area, realizes higher electric power injection of the CO2 laser amplifier, and obtains higher laser power output.

[0049] The present application is described in detail below with reference to the accompanying drawings.

[0050] like Figure 1As shown, the present application proposes a method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier, wherein the laser amplifier is applied to an extreme ultraviolet lithography light source, and the method comprises the following steps:

[0051] Step S102: Construct the electrode width of the laser amplifier in the downstream direction from the starting position x The radian function at :

[0052]

[0053] in, k is the electrostatic force constant, Indicates the wall thickness of the glass discharge tube. is the electric power injection at the starting position of the discharge area, k B is the Boltzmann constant, L 0 is the total length of the electrode ω is the RF angular frequency, ε is the dielectric constant of quartz glass, L 0 is the total length of the electrode, a is the discharge threshold, P is the discharge gas pressure, d is the discharge distance, U 0 is the discharge electrode voltage, C 气体 is the specific heat capacity of the gas, v 气体 is the gas flow rate, S is the cross-sectional area of ​​the discharge glass tube, is the gas density, is the gas temperature at the starting position of the discharge region;

[0054] Step S104: Distance from the electrode width to the starting position x The radian function at The electrode structure is designed so that the electrode extends in an axial spiral and the arc corresponding to the electrode width along the axial direction increases gradually.

[0055] In step S102, the electrode width of the laser amplifier along the axial downstream direction is specifically constructed from the starting position x The radian function at The process is as follows:

[0056] During the operation of the laser amplifier, a cooling system is added to the flow field cycle to reduce the temperature of the high-temperature gas coming out of the downwind outlet and then circulate it back to the upwind outlet to ensure that the temperature of the upwind outlet of the discharge system remains stable. Due to the energy deposition of the RF power during operation, the downwind outlet temperature gradually increases and finally remains stable. In order to ensure laser gain, the E / N ratio of the entire discharge area must be kept as consistent as possible. x The temperature at can be expressed as:

[0057]

[0058] in, P x is the axial distance of the discharge area x The electric power injection at the upwind side is x=0, T x is the gas temperature at a distance x from the upper tuyere along the discharge electrode, C 气体 is the specific heat capacity of the gas, v 气体 is the gas flow rate, S is the cross-sectional area of ​​the discharge glass tube, ρ 气体 is the gas density, and T0 is the temperature at the upwind side.

[0059] The gas state can be expressed by the ideal gas state equation (2) and the gas discharge threshold equation (3):

[0060]

[0061] in, P is the discharge gas pressure, k B is the Boltzmann constant, a is the discharge threshold and is a constant when the discharge conditions are determined. As can be seen from formula (1), increasing the power injection will inevitably lead to an increase in the axial temperature. The thermal expansion of the gas will reduce the particle number density N, causing the ratio E / N of the electric field E to the particle number density N in the discharge region to increase along the axial direction, making the discharge region unevenly distributed along the axial direction and reducing the laser gain.

[0062] In this case, the present application designs a spiral electrode with an increasing axial curvature to reduce the electric field strength E at the downwind outlet of the discharge area and compensate for the increase in E / N due to the temperature gradient between the downwind outlet and the upwind outlet. The spiral electrode designed in the present application can maintain E / N= a . Discharge electrode voltage U 0 The discharge voltage remains unchanged along the axial direction. U x It can be expressed by formula (4) and formula (5),

[0063]

[0064] in, X is the equivalent reactance of the quartz glass tube between the discharge electrodes, R is the equivalent resistance of the discharge plasma, d is the discharge distance, and is expressed by the electrical formula:

[0065]

[0066] It is assumed that the RF power is uniformly injected along the axial direction, where k is the electrostatic force constant, ω=2 πf is the RF angular frequency, ε is the dielectric constant of quartz glass, S’ is the discharge area of ​​the spiral electrode, L 0 is the total length of the electrode, P 0 is the total RF injection power. Substituting Equations (4), (6) and (7) into Equation (5) can solve the spiral electrode surface area: S’ Axial distance x expression

[0067]

[0068] For spiral electrodes , For location x The electrode width D corresponds to the arc, and the electrode width D refers to the distance of the electrode along the direction perpendicular to the axial direction, such as Figure 4 As shown. According to formula (1), the temperature T x It's location x A linear function of . In summary, the axial arc of the spiral electrode can be expressed as the axial distance x Function

[0069]

[0070] For RF axial fast flow CO2 laser amplifiers, the upwind temperature T0 is usually maintained at 25℃ (300K), so in Equation (9) can be ignored, and formula (9) can be expressed as

[0071] (10)

[0072] When the radio frequency power is uniformly injected along the axial direction of the discharge electrode, for x A linear function of Approximately x Linear function of .

[0073]

[0074] Right now:

[0075] It can be seen from the formula that when a certain RF power is uniformly injected, the corresponding curvature of the spiral electrode should increase linearly along the axial distance x to compensate for the decrease in discharge E / N caused by the thermal expansion of the gas.

[0076] In step S104, in some embodiments, the electrodes include a positive electrode extending in an axial spiral and a negative electrode extending in an axial spiral, and the spacing between the positive electrode and the negative electrode is equal in the axial direction.

[0077] like Figure 2 As shown in FIG, the discharge unit of the high-power CO2 laser amplifier consists of a pair of discharge electrodes 3, a discharge glass tube 5, and a polytetrafluoroethylene electrode holder 4. The two ends of the pair of discharge electrodes 3 are respectively clamped on the polytetrafluoroethylene electrode holders 4 on both sides. The electrodes 3 include a positive electrode extending in an axial spiral and a negative electrode extending in an axial spiral. The positive electrode and the negative electrode are symmetrically arranged on the outside of the discharge tube, as shown in FIG. Figure 4 Specifically, Figure 3 As shown, the positive electrode and the negative electrode are sheet-like structures with a certain width and increasing width in the flat state. For example, the width of the terminal end 32 is greater than the width of the starting end 31 and the electrode 3 is twisted at a certain angle along the circumference to form a spiral electrode structure, as shown in FIG. Figure 3 As shown, the terminating end 32 and the starting end 31 are then respectively fixed to the polytetrafluoroethylene electrode holder 4, thereby forming a positive electrode and a negative electrode extending in an axial spiral. At the same time, the positive electrode and the negative electrode are twisted so that the distance between the positive electrode and the negative electrode is equal in the axial direction to form a stable discharge electric field.

[0078] Optionally, the curvature of the electrode from the starting end to the ending end is equal, and is substantially the same as the curvature of the discharge tube.

[0079] Optionally, the widths of the positive electrode and the negative electrode from the starting end to the ending end are symmetrically equal along the center of the discharge tube, so as to form a stable electric field between the positive electrode and the negative electrode.

[0080] In some embodiments, the electrode includes a starting end 31 and an ending end 32 that extend in an axial spiral. The circumferential extension of the starting end 31 to the ending end 32 is less than 360 degrees. In other words, the electrode is twisted circumferentially for no more than one revolution. Optionally, the circumferential extension angle of the starting end to the ending end is less than 180 degrees, for example, less than 90 degrees, to avoid electrode charging that could affect gas discharge.

[0081] In some embodiments, under a power injection of 10 kW, the arc of the electrode starting end is 15 degrees, and the arc at a distance of 220 mm downstream is 20 degrees. This ensures that the thermal effect of the discharge module in the CO2 laser amplifier has a consistent effect on the E / N ratio of the discharge area.

[0082] This application proposes a method for designing electrodes to compensate for temperature gradient effects in CO2 laser amplifiers through theoretical derivation. This method results in an electrode structure in which the electrode extends in a spiral axial direction, with the arc increasing along the axial electrode width. By designing a spiral electrode structure with an increasing arc along the gas flow direction, this application achieves an axial change in the electric field strength E in the discharge region to compensate for the decrease in gas particle density N caused by axial thermal effects, maintain the discharge condition E / N at a certain level, and reduce the impact of axial temperature gradients on the uniformity of axial gas discharge.

[0083] Finally, it should be noted that the various embodiments in this specification are described by way of example. Each embodiment focuses on the differences from other embodiments, and reference can be made to the common and similar parts between the various embodiments. For the systems or devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For relevant details, refer to the description of the methods.

[0084] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for designing a temperature gradient effect compensation electrode for a CO2 laser amplifier, wherein the laser amplifier is used as an extreme ultraviolet lithography light source, characterized in that: include: Construct the electrode width of the laser amplifier along the axial downstream direction from the starting position x The radian function at : in, k is the electrostatic force constant, Indicates the wall thickness of the glass discharge tube. is the electric power injection at the starting position of the discharge area, k B is the Boltzmann constant, ω is the RF angular frequency, ε is the dielectric constant of quartz glass, L 0 is the total length of the electrode, a is the discharge threshold, P is the discharge gas pressure, d is the discharge distance, U 0 is the discharge electrode voltage, C 气体 is the specific heat capacity of the gas, v 气体 is the gas flow rate, S is the cross-sectional area of ​​the discharge glass tube, is the gas density, is the gas temperature at the starting position of the discharge region; According to the electrode width distance from the starting position x The radian function at The electrode structure is designed so that the electrode extends in an axial spiral and the arc corresponding to the electrode width along the axial direction increases gradually.

2. The method according to claim 1, characterized in that The electrodes include a positive electrode extending in a spiral along the axial direction and a negative electrode extending in a spiral along the axial direction, and a distance between the positive electrode and the negative electrode remains unchanged in the axial direction.

3. The method according to claim 2, characterized in that The positive electrode and the negative electrode are symmetrically arranged outside the discharge tube.

4. The method according to claim 1, wherein The electrode comprises a starting end and an ending end extending in an axial spiral, and the spiral extension angle from the starting end to the ending end in the circumferential direction is less than 360 degrees.

5. The method according to claim 4, characterized in that The spiral extension angle from the starting end to the ending end in the circumferential direction is less than 180 degrees.

6. The method according to claim 4, characterized in that The curvature of the electrode from the starting end to the ending end is equal.

7. The method according to claim 2, characterized in that The widths of the positive electrode and the negative electrode from the starting end to the ending end are symmetrically equal along the center of the discharge tube.

8. The method according to claim 2, characterized in that The width of the positive electrode and the negative electrode at the starting end is smaller than the width of the ending end in a flattened state.

9. The method according to claim 1, characterized in that Under a power injection of 10 kW, the arc of the electrode starting end is 15 degrees, and the arc at a distance of 220 mm downstream is 20 degrees.

10. The method according to claim 1, characterized in that The electrode width of the laser amplifier in the downstream direction is the distance from the starting position to the x The radian function at ,include: Constructing the laser amplifier along the axial distance x Temperature gradient function at : in, P x The axial distance of the discharge area from the starting position x The electric power injection at T x The axial distance of the discharge area from the starting position x The gas temperature at is the gas temperature at the starting position of the discharge region; Constructing spiral electrode along the axial distance x The radian function at Temperature gradient function Relationship: Ignore the temperature quartic term Then, the electrode width of the laser amplifier in the downstream direction is obtained from the starting position. x The radian function at : 。

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